Magnetoencephalography (MEG) and related electroencephalography (EEG) use an array of sensors to non-invasively measure electromagnetic (EM) fields produced by synchronous current activity within the brain. While the temporal resolution is excellent relative to other functional imaging modalities, accurately localizing in 3D space the sources of brain activity involves solving a difficult, underdetermined inverse problem. Existing localization methods used clinically and for research purposes maintain significant shortcomings, including the inability to resolve complex source configurations, bias caused by source correlations, and sensitivity to sources of noise and interference. The latter can arise from eye blinks, heart beats, sensor imperfections, and industrial noise as well as from spontaneous background brain activity not associated with the brain sources of interest. Additionally, prototype algorithms ostensibly designed to deal with some of these issues are heuristic in nature and have not been rigorously evaluated or compared, making their ultimate utility difficult to assess for neuroelectromagnetic imaging practitioners. The proposed research plan addresses all of these concerns by developing a principled localization scheme that unifies and extends existing localization strategies using modern concepts from Bayesian statistics and machine learning. Based on the notion of automatic relevance determination (ARD), brain regions with probable (relevant) activity are located with high spatial resolution. Interference sources are effectively removed by integrating with a variation factor analysis model. To quantify the improvement afforded by the proposed methodology, source location estimates will be compared with standard algorithms using realistic simulations, near-ground-truth data obtained from invasive electrocorticographic (ECoG) recordings, and surgical data. The result will be implemented as a user-friendly localization toolbox and made freely available to the community by integrating with existing open-source functional brain imaging software. Non-invasive mapping of brain activity with high spatio-temporal resolution has important consequences for basic neuroscience studies of human cognition. It also has profound implications for the diagnosis, characterization and treatment of various neurological, neurooncological, mental health, developmental, and communication disorders. For example, localizations of brain sources are used to map cognitive function in epileptogenic areas and in neighboring brain regions. Such brain mapping procedures are then useful to guide neurosurgical planning, navigation, and resection and to minimize post-operative deficits.